Problem: Multiply.
When a number is next to a variable, it means they are multiplied. So, $({4}{z^3})({-3}{z^3})$ is the same as $({4})({z^3})({-3})({z^3})$. Now we can rearrange the factors because multiplication is commutative (a fancy way of saying that the order in which we multiply things doesn't matter). ${(4)(-3)}{(z^3)(z^3)}$ Then simplify, and we're done! ${-12}{z^6}$